Problem 11 · 2010 Math Kangaroo
Medium
Number Theory
divisibility
Grandma has baked a cake for her grandchildren. She does not know whether 3, 5, or all 6 grandchildren will come today. Into how many pieces does she have to cut the cake so that, no matter how many come, all the grandchildren present get the same amount of cake?
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Answer: E — 30
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Hint 1 of 2
The number of pieces must split evenly among 3, 5 or 6 children.
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Hint 2 of 2
So you need the smallest number divisible by all of 3, 5 and 6 — their least common multiple.
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Approach: least common multiple
- The pieces must divide evenly by 3, by 5 and by 6.
- LCM(3,5,6) = 30, so she cuts the cake into 30 pieces.
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